Some representations of midconvex set-valued functions.
Some results on stability and on characterization of K-convexity of set-valued functions
We present a stability theorem of Ulam-Hyers type for K-convex set-valued functions, and prove that a set-valued function is K-convex if and only if it is K-midconvex and K-quasiconvex.
Spline Subdivision Schemes for Compact Sets. A Survey
Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, IsraelAttempts at extending spline subdivision schemes to operate on compact sets are reviewed. The aim is to develop a procedure for approximating a set-valued function with compact images from a finite set of its samples. This is motivated by the problem of reconstructing a 3D object from...
The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive Banach spaces.
The intersection convolution of relations and the Hahn-Banach type theorems
By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an...
Uniformly Continuous Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz
We show that any uniformly continuous and convex compact valued Nemytskiĭ composition operator acting in the spaces of functions of bounded φ-variation in the sense of Riesz is generated by an affine function.
Upper quasi continuous maps and quasi continuous selections
The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form , where is open and , are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form .
Variation preserving extensions and generalized essential variation.
Инфинитезимальный локальный оптимум функции множества
О множествах неоднозначности монотонных отображений и отображений спроса.
Почти периодические многозначные отображения и их сечения.